4.16.40 \(y'(x)^2-(x+1) y'(x)+y(x)=0\)

ODE
\[ y'(x)^2-(x+1) y'(x)+y(x)=0 \] ODE Classification

[[_1st_order, _with_linear_symmetries], _Clairaut]

Book solution method
Clairaut’s equation and related types, main form

Mathematica
cpu = 0.00241427 (sec), leaf count = 15

\[\left \{\left \{y(x)\to c_1 \left (-c_1+x+1\right )\right \}\right \}\]

Maple
cpu = 0.018 (sec), leaf count = 22

\[ \left \{ y \relax (x ) ={\it \_C1}\, \left (-{\it \_C1}+x+1 \right ) ,y \relax (x ) ={\frac { \left (1+x \right ) ^{2}}{4}} \right \} \] Mathematica raw input

DSolve[y[x] - (1 + x)*y'[x] + y'[x]^2 == 0,y[x],x]

Mathematica raw output

{{y[x] -> (1 + x - C[1])*C[1]}}

Maple raw input

dsolve(diff(y(x),x)^2-(1+x)*diff(y(x),x)+y(x) = 0, y(x),'implicit')

Maple raw output

y(x) = 1/4*(1+x)^2, y(x) = _C1*(-_C1+x+1)